• University of Michigan

• CHEM 125 CHEM 125 General Chemistry Lab Chem 125 Lab 1

Lab 1: Measurement and Uncertainty

Chem 125/126 Section 194/195
Introduction: While studying the sciences, it is important to take into account the accuracy and
precision of your measurements. Significant figures allow scientists to express that they have
measured all certain digits plus the first uncertain digit. Uncertainty accounts for systematic and
random errors that may occur during the experimental process. Therefore, it is important that
scientists calculate the uncertainty in a specific measurement as well in order to have the most
accurate value possible.
Objectives/Hypothesis: In this lab, we are trying to identify the material of a cube object based
on the most accurate measurements we take of its volume and mass using a Vernier caliper and
ruler. If we take into account the accuracy and precision that are essential for taking accurate
measurements and uncertainty, we will determine the material of each cube by using a Vernier
caliper.
Materials/Methods: In this lab, we used 10 different blocks each composed of a different
material. To measure these blocks, we used a scale to measure the mass of each cube in grams,
and to measure the volume, we used both a ruler and a Vernier caliper. After first gathering our
materials, we took accurate measurements of each cube by individually weighing it on the scale.
After determining the cube’s mass, we used a ruler to measure the length, width, and height of
the cube. With these measurements, we were able to determine the volume of the cube. We
repeated this step again but instead with the Vernier caliper.
Sample Calculation:
Mass of cube = 130.801 grams
Uncertainty of mass = (least count/2) = (0.001grams/2) = 0.0005 grams
Length of cube (Vernier caliper) = 2.51 cm
Width of cube (Vernier Caliper) = 2.51 cm
Height of cube (Vernier Caliper) = 2.60 cm
Volume of cube = length*width*height = 2.51cm*2.51cm*2.60cm = 16.38026cm3
Uncertainty of volume = (least count/2) = (.001cm/2) = 0.0025 cm
Density = mass/volume = 130.801g/16.38026cm3 = 7.98528228 g/cm3
Formula for error propagation =
( ∆ x
x
2
)
(¿+( ∆ y
y
2
))
∆ z=z √¿
z=measurement (density)x=first measurement (mass)
y=second measurement(volume)
∆ x=uncertainty of measurement x∆ y=uncertainty of measurement y
∆ z=7.98528228√130.801 0.0005 2+ 16.38026 0.0025 2
∆ z=0.001219118
Density of Cube 1: 7.98528+-0.001219 g/cm

Work Cited
"Densities." Plexus-IEM. Plexus-IEM, n.d. Web. 25 Jan. 2016.